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2x^{2}-2x-3
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2x^{2}-2x-3
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6x^{2}-15x-\left(x-3\right)\left(4x-1\right)
Use the distributive property to multiply 3x by 2x-5.
6x^{2}-15x-\left(4x^{2}-x-12x+3\right)
Apply the distributive property by multiplying each term of x-3 by each term of 4x-1.
6x^{2}-15x-\left(4x^{2}-13x+3\right)
Combine -x and -12x to get -13x.
6x^{2}-15x-4x^{2}-\left(-13x\right)-3
To find the opposite of 4x^{2}-13x+3, find the opposite of each term.
6x^{2}-15x-4x^{2}+13x-3
The opposite of -13x is 13x.
2x^{2}-15x+13x-3
Combine 6x^{2} and -4x^{2} to get 2x^{2}.
2x^{2}-2x-3
Combine -15x and 13x to get -2x.
6x^{2}-15x-\left(x-3\right)\left(4x-1\right)
Use the distributive property to multiply 3x by 2x-5.
6x^{2}-15x-\left(4x^{2}-x-12x+3\right)
Apply the distributive property by multiplying each term of x-3 by each term of 4x-1.
6x^{2}-15x-\left(4x^{2}-13x+3\right)
Combine -x and -12x to get -13x.
6x^{2}-15x-4x^{2}-\left(-13x\right)-3
To find the opposite of 4x^{2}-13x+3, find the opposite of each term.
6x^{2}-15x-4x^{2}+13x-3
The opposite of -13x is 13x.
2x^{2}-15x+13x-3
Combine 6x^{2} and -4x^{2} to get 2x^{2}.
2x^{2}-2x-3
Combine -15x and 13x to get -2x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}